Thermodynamics and statistical mechanics 1

Syllabus

• Main concepts of Statistical Physics: separation of microscopic and macroscopic description of a system; microstates vs. configurations; sharpness of the distribution of microstates over configuration space; basic idea of statistical ensembles and of probabilities.
• Main concepts of Statistical Physics as applied to a simple modelsystem of two-state spins: numbering of microscopic states; multiplicity function; continuous approximation of the multiplicity function; probabilities of micro- and macro- states; characteristics of probability function, mean, variance and standard deviation; sharpness of the probability distribution of a macroscopic variable; correlation of two random variables.  
• Microcanonical ensemble: probabilities of microscopic states in an isolated system at equilibrium; example of equilibration in the system of spins; thermal equilibrium of two arbitrary systems; definition of temperature; entropy in microcanonical ensemble; additivity of entropy; the postulate of entropy increase in an isolated system (second Law of Thermodynamics); the direction of heat flow.
• Canonical ensemble: Boltzmann Distribution; partition function; microscopic state probabilities; average energy of a system in thermal equilibrium; fluctuations in energy and their relation to heat capacity; Helmoholtz Free energy and its relation to the partition function.
• Applications of the canonical ensemble: the system of spins; Schottky anomaly; partition function, energy and free energy of a classical
  ideal monoatomic gas.   
• Thermodynamic equilibrium and thermodynamic processes; characteristic time scales; reversible and irreversible processes; quasi-stationary process; examples of quasi-stationary heat transfer and of work.
  
•  Heat and Work in thermodynamics; First Law of Thermodynamics; differential relations between thermodynamic quantities; Maxwell relations; enthalpy; heat capacity; intensive and extensive quantities; entropy, pressure and heat capacity of a classical ideal monoatomic gas.  
•  More applications of Canonical ensemble: classical oscillators, single and coupled; normal modes in the linear beads-springs system; Equipartition Theorem.  
• Thermal Radiation: experimental facts about thermal radiation; Wien's law; Stephan-Boltzmann law; classical description of electromagnetic field;  Ultraviolet Catastrophe; quantum oscillator; Plank thermal radiation law; photons.  
• Heat capacity of solids: Dulong-Petit law; classical treatment of the problem; deviations from Dulong-Petit law;  Einstein theory of heat capacity; Einstein temperature; Debye theory; Debye temperature; phonons; heat capacity of diatomic gas.
•  Grand Canonical ensemble: chemical potential; Gibbs Distribution; grand partition function; grand thermodynamic potential and its relation to grand partition function; average number of molecules and fluctuations in the number of molecules in the system at thermal and diffusive equilibrium; Maxwell relations for chemical potential.    
• Applications of Grand Canonical ensemble: external chemical potential; distribution of molecules in atmosphere; equilibrium between adsorbed molecules and gas.
• Heat Engines: perpetuum mobile of first and second type; Kelvin-Planck and Clausius formulations of second law of Termodynamics; PV-diagram of processes in a heat engine; efficiency of a heat engine; isothermal, isobaric, isochoric and adiabatic processes; Carnot cycle;refrigerators. 
  
• Summary of Statistical Mechanics and Thermodynamics I; centrality of the Second Law of Thermodynamics in physics and other disciplines; Maxwell demon.

Sources:

1. C. Kittel and H. Kroemer, Thermal Physics
2. F. Reif F, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, NY 1965, QC 175.R43